SUMMARY
Currently, a wide class of modern wireless telecommunications systems is based on the use of broadband signals. The problems of synthesis for their formation and processing algorithm are extremely important for such systems, especially under the conditions of various types of disturbances, which is impossible without scientifically based analysis of signal properties. The article presents the results of signal property and synthesis sub-band analysis obtained by the division of the Fourier cosine transformation (transformants) definition domain for signal record into sub-bands (frequency representations). It is shown that the basis of the mathematical apparatus proposed for sub-band analysis and signal synthesis is a new class of matrices, called sub-band ones. The use of this mathematical apparatus allows to solve the tasks of sub-band analysis and signal synthesis without the transfer to the cosine transformation definition domain (without its calculation, but in the signal definition domain directly).Some properties of the eigenvalues for these matrices are established; the problem of additive signal component optimal selection is formulated and solved.